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  <title>2022美赛总结 | 鲨鱼之家</title>
  <meta name="description" content="前言 题目描述_Trading Strategies  Background Requirement   题目分析 我们的模型  预测模型 决策模型 Our Summary of the Paper   体会  关于团队合作 关于怎么准备美赛 其他     前言 距离2022年2月18日开始的美赛已经过去一周多，本来计划美赛一结束就写一篇总结和体会的，结果因为各种原因~~（才不是因为懒，笑.j">
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        <!-- toc -->
<ul>
<li><a href="#%E5%89%8D%E8%A8%80">前言</a></li>
<li><a href="#%E9%A2%98%E7%9B%AE%E6%8F%8F%E8%BF%B0_trading-strategies">题目描述_Trading Strategies</a>
<ul>
<li><a href="#background">Background</a></li>
<li><a href="#requirement">Requirement</a></li>
</ul>
</li>
<li><a href="#%E9%A2%98%E7%9B%AE%E5%88%86%E6%9E%90">题目分析</a></li>
<li><a href="#%E6%88%91%E4%BB%AC%E7%9A%84%E6%A8%A1%E5%9E%8B">我们的模型</a>
<ul>
<li><a href="#%E9%A2%84%E6%B5%8B%E6%A8%A1%E5%9E%8B">预测模型</a></li>
<li><a href="#%E5%86%B3%E7%AD%96%E6%A8%A1%E5%9E%8B">决策模型</a></li>
<li><a href="#our-summary-of-the-paper">Our Summary of the Paper</a></li>
</ul>
</li>
<li><a href="#%E4%BD%93%E4%BC%9A">体会</a>
<ul>
<li><a href="#%E5%85%B3%E4%BA%8E%E5%9B%A2%E9%98%9F%E5%90%88%E4%BD%9C">关于团队合作</a></li>
<li><a href="#%E5%85%B3%E4%BA%8E%E6%80%8E%E4%B9%88%E5%87%86%E5%A4%87%E7%BE%8E%E8%B5%9B">关于怎么准备美赛</a></li>
<li><a href="#%E5%85%B6%E4%BB%96">其他</a></li>
</ul>
</li>
</ul>
<!-- tocstop -->
<h2><span id="前言">前言</span></h2>
<p>距离2022年2月18日开始的美赛已经过去一周多，本来计划美赛一结束就写一篇总结和体会的，结果因为各种原因~~（才不是因为懒，笑.jpg）~~，拖到了今天，话不多说，直接开始吧！</p>
<ul>
<li>分工：一位同学负责论文，我和另外一位同学负责建模和编程；期间我还参与了一小部分论文的翻译和润色。</li>
<li>选题：<font color="red">C题_Trading Strategies</font>。赛前打算从A、C、D题里面选，但是内心里面是偏向C题的，因为C题描述和要求都非常明确，且数据集给定，不需要太多搜集资料的时间（事实证明C题一样得查很多资料）；比赛当天早上看到题目之后，我们队伍毫不犹豫地选择了C题。</li>
</ul>
<h2><span id="题目描述_trading-strategies">题目描述_Trading Strategies</span></h2>
<h3><span id="background">Background</span></h3>
<p>Market traders buy and sell volatile assets frequently, with a goal to maximize their total return. There is usually a commission for each purchase and sale. Two such assets are gold and bitcoin.</p>
<div align="center"><img src="https://gitee.com/tina-yao/bigbig-shark/raw/master/imgs/comap/1.png" width="  "></div>
<h3><span id="requirement">Requirement</span></h3>
<p>You have been asked by a trader to <strong>develop a model that uses only the past stream of daily prices to date to determine each day if the trader should buy, hold, or sell their assets in their portfolio</strong>.  You will start with $1000 on 9/11/2016. You will use the five-year trading period, from 9/11/2016 to 9/10/2021. On each trading day, the trader will have a portfolio consisting of cash, gold, and bitcoin [C, G, B] in U.S. dollars, troy ounces, and bitcoins, respectively. The initial state is [1000, 0, 0]. The commission for each transaction (purchase or sale) costs α% of the amount traded. Assume αgold = 1% and αbitcoin = 2%. There is no cost to hold an asset.  Note that bitcoin can be traded every day, but gold is only traded on days the market is open, as reflected in the pricing data files LBMA-GOLD.csv and BCHAIN-MKPRU.csv. Your model should account for this trading schedule.</p>
<p>To develop your model, you may only use the data in the two spreadsheets provided: LBMA-GOLD.csv and BCHAIN-MKPRU.csv.</p>
<ul>
<li>Develop a model that gives the best daily trading strategy based only on price data up to that day. How much is the initial $1000 investment worth on 9/10/2021 using your model and strategy?</li>
<li>Present evidence that your model provides the best strategy.</li>
<li>Determine how sensitive the strategy is to transaction costs. How do transaction costs affect the strategy and results?</li>
<li>Communicate your strategy, model, and results to the trader in a memorandum of at most two pages.</li>
</ul>
<h2><span id="题目分析">题目分析</span></h2>
<ul>
<li>一个目标：最大化收益</li>
<li>两个对象：黄金和比特币</li>
<li>三种选择：买入、卖出、持有</li>
<li>两个数据集：两个数据集内容都是【时间-当日收盘价格】，其中时间格式不一致，而黄金还存在交易关闭日，这意味着要根据模型进行数据清洗。</li>
<li>注意：
<ul>
<li>每一次交易有手续费</li>
<li>黄金有交易关闭日</li>
</ul>
</li>
</ul>
<h2><span id="我们的模型">我们的模型</span></h2>
<p>核心是一个预测模型+一个决策模型。即首先应用预测模型基于当日之前的收盘价格对未来一段时间的收盘价进行预测；然后应用决策模型基于预测出来的收盘价格数据指导当日的决策，即决策买入、卖出或持有。</p>
<h3><span id="预测模型">预测模型</span></h3>
<p>预测模型使用了<font color="red">等维灰度模型</font>（Equal Dimension Gray Model)。</p>
<p>首先介绍灰度预测模型，灰度预测模型是一种强大的预测模型，是基于原始的数据进行灰度化后找到一种规律后再进行建模的模型，其强大在于将无序、波动大、变化快的原始序列转变为一种有序、有规律的序列。而且用很少的数据就可以完成精度很高的数据预测。它有以下特点：</p>
<ul>
<li>可以将波动大、变化快的无规律数据进行<font color="red">灰度化</font>，将原始数据转化为有规律数据，发现数据内在规律，从而建立模型。</li>
<li>仅仅需要较少数据（n&gt;=4）就可以完成较高精度的预测。</li>
</ul>
<p>考虑到黄金和比特币每日收盘价格具有以下特点：</p>
<ul>
<li>波动大，变化快，因为每天的选择（买入、卖出或持有）都可能起到关键作用而影响到最终受益，所以不能做普通的平滑处理。</li>
<li>虽然黄金和比特币的价格都有一个向上的趋势，但基于每日都要做出选择且数据波动无直接规律，所以我们认为比较久远的收盘价对近期的收盘价格无明显影响以至于可以被忽略不计。</li>
</ul>
<p>所以我们认为选择灰度预测模型进行收盘价的预测是合理可行的。</p>
<p>但是普通灰度预测模型的缺点也不可忽略，<strong>其预测精度会随预测时间的增长而迅速下降</strong>；通俗来说，未来第一天收盘价格的预测精度很高，但可能第二天就一般，第三天勉勉强强，第四天就 不能用了……因为我们的决策模型需要未来一段较长时间的预测数据，所以普通灰度预测模型的这个缺点是致命的。基于此，我们决定使用等维灰度模型。</p>
<p>等维灰度预测模型又叫做新陈代谢模型，顾名思义，喂入等维灰度模型的数据个数是固定的且不断更新。比如说，普通灰度模型直接用第1天到第4天的数据来预测未来多天的数据，但是等维灰度预测模型就会这样做：</p>
<ol>
<li>用第1天到第4天的数据预测出第5天的数据；</li>
<li>删除第1天的数据，加入第5天的数据，这样就保证了被喂入模型的数据的<strong>等维</strong>；</li>
<li>用第2步得到的新的原始数据预测出第6天的数据；</li>
<li>重复以上步骤，直到得到想要的区间。</li>
</ol>
<h3><span id="决策模型">决策模型</span></h3>
<p>决策模型基本思想：</p>
<ul>
<li>因为交易时需要在黄金和比特币之间做出权衡，所以我们使用了线性规划；</li>
<li>前几日因为数据过少（&lt;4），无法进行预测，所以前4日持观望态度；</li>
<li>第5日开始，基于预测数据，我们使用线性规划来计算当日收益（注意手续费），倘若收益为正，就进行交易，否则持有；</li>
<li>持续进行上一步骤，直到得到最终受益；</li>
<li>为了简化模型，我们引入了股票市场常用的日均线，比如说5日均线、15日均线、60日均线等。</li>
</ul>
<p>因为日均线主要是另外一个同学提出引入的，而我没太参与，所以不再赘述。</p>
<h3><span id="our-summary-of-the-paper">Our Summary of the Paper</span></h3>
<p>Gold and Bitcoin are the most eye-catching volatile assets in the trading market and every market trader desires to benefit from them. However, the price data of both gold and Bitcoin shows great fluctuation and rapid changes, which makes it difficult for traders’ investments to pay off.</p>
<p>To address the challenge and relative problems, we proposed a best daily trading strategy called Visible Future Benefits System, consisting of a Price Prediction Model based on the Equal Dimension Gray Model, and also a Strategy Model based on Daily Moving Average and Linear Programming. The main factors that help us to decide on the system are the predicted price data, daily moving average, and the result of linear programming.</p>
<p>In the price prediction model, we introduce the normal gray model and equal dimension gray model to find the inner regular pattern after a series of data processing and forecast the future trend of price data. We first select an n-digit-sequence from the previous original data series and define gray ratio and confidence interval to check if we can apply the model to the data appropriately. Next, we process the data to make it smooth to show the rules. In the short term, the normal gray model is very effective with high accuracy. But as days go on, the accuracy dropped. To solve this problem, we further introduce an equal dimension gray model to modify it. In this model, we updated the ndigit-sequence data set, deleting the first data of the n-digit-sequence and adding the first predicted data to it, hence we get a new n-digit-sequence. In this way, we can repeat performing the gray model and predict the price with satisfying accuracy along with the whole data.</p>
<p>As for the strategy model, based on the predicted price of the prediction model, we define benefit-cost to quantify the benefits we can obtain when we determine to buy, hold or sell the gold or Bitcoin. Moreover, to a make portfolio selection of gold and Bitcoin, we performed linear programming to decide the most appropriate proportion of gold and Bitcoin we should trade. As a result, the combination of benefit-cost and linear programming allows the asset portfolio to increase nicely and be maximized as possible.</p>
<p>Through the test, we found that when any of the values changed, the return would be reduced and could not be maximized. Therefore, our prediction model and strategy model provided the best trading strategy. At the same time to simplify the model, avoid trading too frequently and save time cost, we employed the moving average of the two asset trading prices into the system. By observing the trend of moving average, we can find the right time point to trade, to get the ultimate asset value in cash. To determine the sensitivity of trading strategies to transaction costs, we also performed sensitivity analyses of commission rates and portfolios. The results show that when the commission rate changes, the impact on the strategy model is relatively small, which indicates our model is relatively strong.</p>
<h2><span id="体会">体会</span></h2>
<p>其实以上的都不是我想重点说的，也说得很简略。<strong>体会这部分才是我写这篇博客的初衷</strong>。</p>
<h3><span id="关于团队合作">关于团队合作</span></h3>
<p>在讨论模型时有些许摩擦，但最终达成一致，总体比较和谐。（有一些组因为分歧直接摆烂，不做了）</p>
<p>对于团队合作，我有以下认识：</p>
<ol>
<li>我想按照自己的思路去完成整个模型，但是我个人能力有限，无法打包票和包干；万一后面出问题了怎么办，须知美赛是一个限时赛。我会因此郁闷，说白了还是个人能力有待提高。</li>
<li>个人独自建模时效率非常高，但也很容易进入思维定势跳不出来，一叶障目，短时间内难以自己深入模型发现局限；但是和队友在一起时，很容易就会走向讨论而放下手上的工作，一放就是几小时（还是那句话，须知这是限时赛），但是讨论的优势也是特别明显的，非常有助于深挖模型，发现模型局限并改进。</li>
</ol>
<h3><span id="关于怎么准备美赛">关于怎么准备美赛</span></h3>
<ol>
<li><strong>直接读论文！直接读论文！直接读论文！<strong>直接选择几道题，大概分析题目后或者干脆不分析题目，找到往年的O奖论文直接开始读！不要想着先去学编程或者模型，因为Matlab和数学模型非一日之功（当然论文也非一日之功，只是说先读论文能使你对建模有个整体把握）——Matlab针对不同的领域有不同的特点，什么都不知道直接开始学会浪费大量时间，还有可能根本没学到其在美赛中的重点应用（<s>比如说我，笑.jpg</s>）；而数学模型也是类似的，针对不同的题型，其模型侧重点也不一样，比如说</strong>C题，直接看预测模型</strong>，完全够用了。</li>
<li>当然你有数学建模竞赛经历或者说有充足的时间和精力学完Matlab和数学模型，当我没说上面这段话嘎嘎。</li>
</ol>
<h3><span id="其他">其他</span></h3>
<p>如果这次拿不到奖的话，就还要参加美赛；如果拿奖（一等奖及以上）的话，就不参加同类比赛了哈哈。</p>

      
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